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REGAIN (Regularised Graph Inference)

Project description

develstat covdevel licence PyPI Conda PyPI pyversions Requirements Status


Regularised graph inference across multiple time stamps, considering the influence of latent variables. It inherits functionalities from the scikit-learn package.

Getting started


REGAIN requires:

  • Python (>= 3.6)
  • NumPy (>= 1.8.2)
  • scikit-learn (>= 0.17)

You can install (required) dependencies by running:

pip install -r requirements.txt

To use the parameter selection via gaussian process optimisation, skopt is required.


The simplest way to install regain is using pip

pip install regain

or conda

conda install -c fdtomasi regain

If you'd like to install from source, or want to contribute to the project (e.g. by sending pull requests via github), read on. Clone the repository in GitHub and add it to your $PYTHONPATH.

git clone
cd regain
python develop


A simple example for how to use LTGL.

import numpy as np
from regain.covariance import LatentTimeGraphicalLasso
from regain.datasets import make_dataset
from regain.utils import error_norm_time

data = make_dataset(n_dim_lat=1, n_dim_obs=3)
X = data.X
y = data.y
theta = data.thetas

mdl = LatentTimeGraphicalLasso(max_iter=50).fit(X, y)
print("Error: %.2f" % error_norm_time(theta, mdl.precision_))

IMPORTANT We moved the API to be more consistent with scikit-learn. Now the input of LatentTimeGraphicalLasso is a two-dimensional matrix X with shape (n_samples, n_dimensions), where the belonging of samples to a different index (for example, a different time point) is indicated in y.


REGAIN appeared in the following two publications. For the LatentTimeGraphicalLasso please use

 author = {Tomasi, Federico and Tozzo, Veronica and Salzo, Saverio and Verri, Alessandro},
 title = {Latent Variable Time-varying Network Inference},
 booktitle = {Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery \&\#38; Data Mining},
 series = {KDD '18},
 year = {2018},
 isbn = {978-1-4503-5552-0},
 location = {London, United Kingdom},
 pages = {2338--2346},
 numpages = {9},
 url = {},
 doi = {10.1145/3219819.3220121},
 acmid = {3220121},
 publisher = {ACM},
 address = {New York, NY, USA},
 keywords = {convex optimization, graphical models, latent variables, network inference, time-series},

and for the TimeGraphicalLassoForwardBackward plase use

  title = 	 {Forward-Backward Splitting for Time-Varying Graphical Models},
  author = 	 {Tomasi, Federico and Tozzo, Veronica and Verri, Alessandro and Salzo, Saverio},
  booktitle = 	 {Proceedings of the Ninth International Conference on Probabilistic Graphical Models},
  pages = 	 {475--486},
  year = 	 {2018},
  editor = 	 {Kratochv\'{i}l, V\'{a}clav and Studen\'{y}, Milan},
  volume = 	 {72},
  series = 	 {Proceedings of Machine Learning Research},
  address = 	 {Prague, Czech Republic},
  month = 	 {11--14 Sep},
  publisher = 	 {PMLR},
  pdf = 	 {},
  url = 	 {},
  abstract = 	 {Gaussian graphical models have received much attention in the last years, due to their flexibility and expression power. However, the optimisation of such complex models suffer from computational issues both in terms of convergence rates and memory requirements. Here, we present a forward-backward splitting (FBS) procedure for Gaussian graphical modelling of multivariate time-series which relies on recent theoretical studies ensuring convergence under mild assumptions. Our experiments show that a FBS-based implementation achieves, with very fast convergence rates, optimal results with respect to ground truth and standard methods for dynamical network inference. Optimisation algorithms which are usually exploited for network inference suffer from drawbacks when considering large sets of unknowns. Particularly for increasing data sets and model complexity, we argue for the use of fast and theoretically sound optimisation algorithms to be significant to the graphical modelling community.}

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